One important thing to remember about the institution of slavery at Gortyn, and probably all over Crete, is that this was not a society that acquired slaves from outside. This meant that any increase in the slave population came about because the existing population reproduced.*** It was thus in the interests of slave owners to encourage the formation of families among their slaves. This then resulted in the need for regulations clarifying any complications, usually pertaining to the ownership of slave children and property when two slaves with different masters married.
The Law Code makes a distinction between children of married slaves and unmarried slaves (whether separated from their spouses or never married). The legal concern here probably had to do with the ownership of any children that resulted from the union. If the spouses had different masters, as was evidently not uncommon, the child automatically belonged to the owner of the male slave. If the pair had separated, the man’s master was given the choice of rearing or rejecting the child; if the latter, the child went to the woman’s master. The child of an unmarried slave belonged to her father’s master.
The laws pertaining to property probably held to similar logic. What a slave possessed legally belonged to their owner. Whenever two (or more) people live together, they tend to acquire property between them. The Law Code indicated who should possess what when a couple separated, thus stipulating whose master technically owned that property. While in practice, slaves at Gortyn held possessions, the Law Code gives them no significant rights over them.
*Should the matter of sex with someone else’s female slave come to court, for example, her oath took precedence.
**Although this may well have been seen as a crime against their (the language in the Code is not gendered) master rather than against the slave.
***Unsurprisingly, slave owners at Gortyn were uninterested in slave breeding. Not only did not doing this allow them to pretend to holding some amount of moral high ground, especially in the event of a slave revolt, but it also significantly cut down the likelihood of such a revolt taking place. The fact that they allowed their slaves to marry other slaves with different masters, and seemingly free women as well (most likely poor freedwomen) was likely a concession to this.
The Law Code of Gortyn (Crete), c. 450 BCE - Internet History Sourcebooks Project
Laws Relating to Women in Gortyn, Crete - Diotima
Lewis, David. "Slave Marriages in the Laws of Gortyn: A Matter of Rights?" Historia 62.4 (2013): 390-416.
Pomeroy, Sarah. Goddesses, Whores, Wives, and Slaves: Women in Classical Antiquity. New York: Pantheon Books, 1995.